Center cyclicity of a family of quartic polynomial differential system

Isaac A. García, Jaume Llibre, Susanna Maza

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2 Citations (Scopus)


© 2016, Springer International Publishing. In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as (Formula presented.), where A, B, C∈ C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.
Original languageEnglish
Article number34
JournalNonlinear Differential Equations and Applications
Issue number3
Publication statusPublished - 1 Jun 2016


  • Bautin ideal
  • Center
  • cyclicity
  • limit cycle
  • polynomial vector fields


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